Testing for nonlinearity of streamflow processes at different timescales

Streamflow processes are commonly accepted as nonlinear. However, it is not clear what kind of nonlinearity is acting underlying the streamflow processes and how strong the nonlinearity is for the streamflow processes at different timescales. Streamflow data of four rivers are investigated in order to study the character and type of nonlinearity that are present in the streamflow dynamics. The analysis focuses on four characteristic time scales (i.e. one year, one month, 1/3 month and one day), with BDS test to detect for the existence of general nonlinearity and the correlation exponent analysis method to test for the existence of a special case of nonlinearity, i.e. low dimensional chaos. At the same time, the power of the BDS test as well as the importance of removing seasonality from data for testing nonlinearity are discussed. It is found that there are stronger and more complicated nonlinear mechanisms acting at small timescales than at larger timescales. All annual series are linear, whereas all daily series are nonlinear. As the timescale increases from a day to a year, the nonlinearity weakens, and the nonlinearity of some 1/3-monthly and monthly streamflow series may be dominated by the effects of seasonal variance. While nonlinear behaviour seemed to be present with different intensity at the various time scales, the dynamics would not seem to be associable to the presence of low dimensional chaos.

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